Spatial discretization of an impulsive Cohen-Grossberg neural network with time-varying and distributed delays and reaction-diffusion terms.
In this work, we consider the singular Hahn difference equation of the Sturm-Liouville type. We prove the existence of the spectral function for this equation. We establish Parseval equality and an expansion formula for this equation on a semi-unbounded interval.
We consider the summation equation, for , in the case where the map may change sign; here is a parameter, which may be understood as the order of an associated discrete fractional boundary value problem. In spite of the fact that is allowed to change sign, by introducing a new cone we are able to establish the existence of at least one positive solution to this problem by imposing some growth conditions on the functions and . Finally, as an application of the abstract existence result,...